your betta may not like the filter moving its water around though. bettas tend to like still water. i had a 10gal tank with some corydora and amano shrimp and a filter that wasn't very stron at all, and when i first got Eric, i put him in there, thinking he'd have plenty of space and be happy, but he just stayed in the corner farthest away from the filter and moving water and wouldnt eat or anything all.
until i took him out, and put him in his own little set up with just him, did he start becoming happy and his personality started to really show.
just something to let you know. i hope he does like the filter though, it would make tank cleaning easier.